Workshops related to Programs which fall into one of the following three categories.

Introductory Workshop: The idea of these workshops is to set the stage and
provide the context for the program, with the intended audience being
researchers notin the program. This would include members
in the other programs, members of the local mathematical community, and
participants from outside the area selected especially for the workshop,
particularly from groups underrepresented in research intensive contexts:
women, minorities, mathematicians not located at research centers, and graduate
students. In selecting participants, priority is given to these latter
groups. When done well, these introductory workshops have been effective
in broadcasting the goals, ideas and techniques of a particular program to the
mathematical public at large, as well as in bringing the MSRI community together
as a whole.

Connections for Women:This
is a two-day workshop held immediately preceding the week of the Introductory
Workshop. While different programs have approached these workshops in
diverse ways, one of the principal objectives, strongly supported by the SAC
and HRAC, is to provide an enhanced opportunity for female researchers to
interact with other women with similar research interests. There is
considerable flexibility for the organization of this two-day event, but MSRI
does require good coordination between the Connections and Introductory
workshop organizers so that as many female researchers as possible are
supported to stay on for the Introductory Workshop.. It is therefore
customary to have one person be simultaneously on the organizing committees for
both of these workshops. As is the case for all MSRI workshops, registration to
attend Connections workshop lectures is open to all interested persons.

Topical
Workshop: Also
directed toward the mathematical community at large, these workshops are designed to interest and
attract young researchers and other mathematicians active in the field.

Our mathematics education system is inequitable. It operates in ways that leave a significant proportion of students with negative mathematics experiences and inadequate mathematical preparation. The problem is historical and systemic, and the students most disaffected by the current system are overwhelmingly Black and Latino, Indigenous, poor, women, immigrant or first generation college students. If our mathematics community is to sustainably grow and thrive, mathematics education at all levels must be transformed.

This workshop focuses on students for whom we do not yet successfully ensure access to and advancement in mathematics. Sessions will share relevant programmatic efforts and innovative research that have been shown to maintain or increase students’ engagement and interests in mathematics across k-12, undergraduate and graduate education. The sessions will focus particularly on reproducible efforts that affirm those students’ identities and their diverse intellectual resources and lived experiences. These efforts at various levels of mathematics education will highlight ways in which meaningful experiences in mathematics can disrupt ongoing systemic oppression. Participants will leave with conceptual and practical ways to open up and elevate mathematics education where all students thrive.

On March 8-10, 2018, IPAM will host a conference showcasing the achievements of Latinx in the mathematical sciences. The goal of the conference is to encourage Latinx to pursue careers in the mathematical sciences, to promote the advancement of Latinx currently in the discipline, to showcase research being conducted by Latinx at the forefront of their fields, and, finally, to build a community around shared academic interests. The conference will be held on the UCLA campus in Los Angeles, CA. It will begin at noon on Thursday, March 8.

This conference is sponsored by the Mathematical Sciences Institutes Diversity Initiative, with funding from the National Science Foundation Division of Mathematical Sciences.

The homological conjectures in commutative algebra are a network of conjectures that have generated a tremendous amount of activity in the last 50 years. They had largely been resolved for commutative rings that contain a field, but, with the exception of some low dimensional cases, several remained open in mixed characteristic --- until recently, when Yves André announced a proof of Hochster's Direct Summand Conjecture. The progress comes from systematically applying Scholze's theory of perfectoid spaces, which had already shown its value by solving formidable problems in number theory and representation theory. One of the goals of the workshop is to cover the ingredients going into the proofs of the Direct Summand Conjecture.

The purpose of the workshop is to bring together specialists to work on understanding the many-faceted mathematical structures underlying problems in enumerative geometry. Topics represented at the workshop will include: geometric representation theory, supersymmetric gauge theory, string theory, knot theory, and derived geometry, all of which have had a profound effect on the development of modern enumerative geometry.

The workshop will bring together key researchers working in various areas of Group Representation Theory to strengthen the interaction and collaboration between them and to make further progress on a number of basic problems and conjectures in the field. Topics of the workshop include-- Global-local conjectures in the representation theory of finite groups-- Representations and cohomology of simple, algebraic and finite groups-- Connections to Lie theory and categorification, and-- Applications to group theory, number theory, algebraic geometry, and combinatorics.

The Infinite Possibilities Conference (IPC) is a national conference that is designed to promote, educate, encourage and support women of color interested in mathematics and statistics, as a step towards addressing the underrepresentation of African-Americans, Latinas, Native Americans, and Pacific Islanders in these fields.

IPC aims to:

fulfill a need for role models and community-building

provide greater access to information and resources for success in graduate school and beyond

raise awareness of factors that can support or impede underrepresented women in the mathematical sciences

A unique gathering, the conference brings together participants from across the country, at all stages of education and career, for mentoring and mathematics.

This Summer Graduate School will introduce students to the modern theory of the inhomogeneous Cauchy-Riemann equation, the fundamental partial differential equation of Complex Analysis. This theory uses powerful tools of partial differential equations, differential geometry and functional analysis to obtain a refined understanding of holomorphic functions on complex manifolds. Besides students planning to work in complex analysis, this course will be valuable to those planning to study partial differential equations, complex differential and algebraic geometry, and operator theory. The exposition will be self-contained and the prerequisites will be kept at a minimum

Higher categorical structures and homotopy methods have made significant influence on geometry in recent years. This summer school is aimed at transferring these ideas and fundamental technical tools to the next generation of mathematicians.

The summer school will focus on the following four topics: higher categorical structures in geometry, derived geometry, factorization algebras, and their application in physics. There will be eight to ten mini courses on these topics, including mini courses led by Chirs Brav, Kevin Costello, Jacob Lurie, and Ezra Getzler. The prerequisites will be kept at a minimum, however, a introductory courses in differential geometry, algebraic topology and abstract algebra are recommended.

The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

In 2018, MSRI-UP will focus on the core role of (linear) algebra in current research and application areas of Data Science ranging from unsupervised learning, clustering and networks, to algebraic signal processing and feature extraction, to the central role linear algebra plays in deep machine learning. The research program will be led by Dr. David Uminsky, Associate Professor of Mathematics and Statistics at the University of San Francisco.

Jointly hosted by Janelia and the Mathematical Sciences Research Institute (MSRI), this program will bring together 15-20 advanced PhD students with complementary expertise who are interested in working at the interface of mathematics and biology. Emphasis will be placed on linking behavior to neural dynamics and exploring the coupling between these processes and the natural sensory environment of the organism. The aim is to educate a new type of global scientist that will work collaboratively in tackling complex problems in cellular, circuit and behavioral biology by combining experimental and computational techniques with rigorous mathematics and physics.

The goal of the school is to give an introduction to basic techniques for working with derived categories, with an emphasis on the derived categories of coherent sheaves on algebraic varieties. A particular goal will be to understand Orlov’s equivalence relating the derived category of a projective hypersurface with matrix factorizations of the corresponding polynomial.

The image of a large sphere isometrically embedded into a small space through a C^1 embedding. (Attributions: E. Bartzos, V. Borrelli, R. Denis, F. Lazarus, D. Rohmer, B. Thibert)

This two week summer school will introduce graduate students to the theory of h-principles. After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, and foliation theory.

Harmonic analysis is a central field of mathematics with a number of applications to geometry, partial differential equations, probability, and number theory, as well as physics, biology, and engineering. The Graduate Summer School will feature mini-courses in geometric measure theory, homogenization, localization, free boundary problems, and partial differential equations as they apply to questions in or draw techniques from harmonic analysis. The goal of the program is to bring together students and researchers at all levels interested in these areas to share exciting recent developments in these subjects, stimulate further interactions, and inspire the new generation to pursue research in harmonic analysis and its applications.

In today's world, data is exploding at a faster rate than computer architectures can handle. This summer school will introduce students to modern and innovative mathematical techniques that address this phenomenon. Hands-on topics will include data mining, compression, classification, topic modeling, large-scale stochastic optimization, and more.

The purpose of the summer school is to introduce graduate students to state-of-the-art methods and results in Hamiltonian systems and symplectic geometry. We focus on recent developments on the study of chaotic motion in Hamiltonian systems and its applications to models in Celestial Mechanics.

This workshop will feature lectures on a variety of topics in Hamiltonian dynamics given by leading researchers in the area. The talks will focus on recent developments in subjects closely related to the program such as Arnold diffusion, celestial mechanics, Hamilton-Jacobi equations, KAM methods, Aubry-Mather theory and symplectic topological techniques, and on applications. The workshop is open to all mathematicians in areas related to the program.

The fascinating and complicated microstructures of materials that are now visible through advanced imaging techniques challenge the frontiers of characterisation and understanding. At the same time, developments in modern geometric and topological techniques are beginning to illuminate important features of material structures, while the microstructures themselves and the analysis and prediction of their macroscopic properties are inspiring new directions in pure and applied mathematics. In a collaboration with the Lawrence Berkeley National Laboratory (LBNL), this workshop aims at intensifying the interaction of mathematicians with material scientists, physicists and chemists on the structural description and design of materials.

This is a main workshop of the program “Hamiltonian systems, from topology to applications through analysis” and is a companion to the workshop next month (November 26-30). Both workshops will feature current developments pertaining to finite and infinite-dimensional Hamiltonian systems, with a mix of rigorous theory and applications. A broad range of topics will be included, e.g., existence of and transport about invariant sets (Arnold diffusion, KAM, etc.), techniques for projection/reduction of infinite to finite systems, and the role of topological invariants in applications.

An invariant set inhibiting transport in a two degree-of-freedom Hamiltonian system (courtesy J. D. Szezech)

This is a main workshop of the program “Hamiltonian systems, from topology to applications through analysis.” It will feature current developments pertaining to finite and infinite-dimensional Hamiltonian systems, with a mix of rigorous theory and applications. A broad range of topics will be included, e.g., existence of and transport about invariant sets (Arnold diffusion, KAM, etc.), techniques for projection/reduction of infinite to finite systems, and the role of topological invariants in applications.

This workshop will be on different aspects of Algebraic Geometry relating Derived Algebraic Geometry and Birational Geometry. In particular the workshop will focus on connections to other branches of mathematics and open problems. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.

The workshop will survey several areas of algebraic geometry, providing an introduction to the two main programs hosted by MSRI in Spring 2019. It will consist of 7 expository mini-courses and 7 separate lectures, each given by top experts in the field.

The focus of the workshop will be the recent progress in derived algebraic geometry, birational geometry and moduli spaces. The lectures will be aimed at a wide audience including advanced graduate students and postdocs with a background in algebraic geometry.

This workshop will bring together researchers at various frontiers, including arithmetic geometry, representation theory, mathematical physics, and homotopy theory, where derived algebraic geometry has had recent impact. The aim will be to explain the ideas and tools behind recent progress and to advertise appealing questions. A focus will be on moduli spaces, for example of principal bundles with decorations as arise in many settings, and their natural structures.

This workshop will be focused on presenting the latest developments in moduli theory, including (but not restricted to) recent advances in compactifications of moduli spaces of higher dimensional varieties, the birational geometry of moduli spaces, abstract methods including stacks, stability criteria, and applications in other disciplines.

Symplectic topology is a fast developing branch of geometry that has seen phenomenal growth in the last twenty years. This two weeks long summer school, organized in the setting of the Séminaire de Mathématiques Supérieures, intends to survey some of the key directions of development in the subject today thus covering: advances in homological mirror symmetry; applications to hamiltonian dynamics; persistent homology phenomena; implications of flexibility and the dichotomy flexibility/rigidity; legendrian contact homology; embedded contact homology and four-dimensional holomorphic techniques and others. With the collaboration of many of the top researchers in the field today, the school intends to serve as an introduction and guideline to students and young researchers who are interested in accessing this diverse subject.

In the past eight years, a number of longstanding open problems in combinatorics were resolved using a new set of algebraic techniques. In this summer school, we will discuss these new techniques as well as some exciting recent developments

Some holomorphic differentials on a genus 2 surface, with close up views of singular points, image courtesy Jian Jiang.

Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In this introductory workshop, we will bring junior and senior researchers from this diverse range of subjects together in order to explore common themes and unexpected connections.

This workshop will provide a gentle introduction to a selection of applications of microlocal analysis. These may be drawn from among geometric microlocal analysis, inverse problems, scattering theory, hyperbolic dynamical systems, quantum chaos and relativity. The workshop will also provide a panel discussion, a poster session and an introduction/research session.

Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This workshop will provide a comprehensive introduction to the field for postdocs and graduate students as well as specialists outside the field, building up from standard facts about the Fourier transform, distributions and basic functional analysis.

The workshop will survey various important and active areas of the representation theory of finite and algebraic groups, and introduce the audience to several basic open problems in the area. It will consist of 6 series of 3 lectures each given by top experts in the field. The lectures are designed for a diverse audience and will be accessible to non-specialists and graduate students with some background in representation theory. Topics covered include Representation theory of algebraic groups, Decomposition numbers of finite groups of Lie type, Deligne-Lusztig theory, Block theory, Categorification, and Local-global-conjectures.

This intensive two day workshop will introduce graduate students and recent PhD’s to some current topics of research in Representation Theory. It will consists of a mixture of survey talks on the hot topics in the area given by leading experts and research talks by junior mathematicians covering subjects such as new developments in character theory, group cohomology, representations of Lie algebras and algebraic groups, geometric representation theory, and categorification.

This workshop will consist of expository mini-courses and lectures introducing various aspects of modern enumerative geometry, among which: enumeration via intersection theory on moduli spaces of curves or sheaves, including Gromov-Witten and Donaldson-Thomas invariants; motivic and K-theoretic refinement of these invariants; and categorical invariants (derived categories of coherent sheaves, Fukaya categories).

The Women in Topology (WIT) network is an international group of female mathematicians interested in homotopy theory whose main goal is to increase the retention of women in the field by providing both unique collaborative research opportunities and mentorship between colleagues. The MSRI WIT meeting will be organized as an afternoon of short talks from participants, followed by two days of open problem seminars and working groups designed to stimulate new collaborations, as well as to strengthen those already ongoing among the participants.

This is the main workshop of the program "Geometric functional analysis and applications". It will focus on the main topics of the program. These include: Convex geometry, Asymptotic geometric analysis, Interaction with computer science, Signal processing, Random matrix theory and other aspects of Probability.

The Bay Area Differential Geometry Seminar meets 3 times each year and is a 1-day seminar on recent developments in differential geometry and geometric analysis, broadly interpreted. Typically, it runs from mid-morning until late afternoon, with 3-4 speakers. Lunch will be available and the final talk will be followed by dinner. Here is the seminar schedule with abstracts and other information: BADG October 2017-Berkeley, CA

As part of the Mathematical Sciences Collaborative Diversity Initiatives, nine mathematics institutes are pleased to offer their annual SACNAS pre-conference event, the 2017 Modern Math Workshop (MMW). The Modern Math Workshop is intended to encourage minority undergraduates to pursue careers in the mathematical sciences and to assist undergraduates, graduate students and recent PhDs in building their research networks. The Modern Math Workshop is part of the SACNAS National Conference; the workshop and the conference take place in the Salt Palace Convention Center in Salt Lake City, Utah. The MMW starts at 1:00 pm on Wednesday, October 18 with registration beginning at noon.

The introductory workshop will present the main topics that will be the subject of much of the Geometric and Topological Combinatorics Program at MSRI. Key areas of interest are point configurations and matroids, hyperplane and subspace arrangements, polytopes and polyhedra, lattices, convex bodies, and sphere packings. This workshop will consist of introductory talks on a variety of topics, intended for a broad audience.

This workshop will feature lectures on a variety of topics in geometric and topological combinatorics, given by prominent women and men in the field. It precedes the introductory workshop and will preview the major research themes of the semester program. There will be a panel discussion focusing on issues particularly relevant to junior researchers, women, and minorities, as well as other social events. This workshop is open to all mathematicians.

This workshop will consist of several short courses related to high dimensional convex geometry, high dimensional probability, and applications in data science. The lectures will be accessible for graduate students.

This workshop will be on topics connected with Asymptotic Geometric Analysis - a relatively new field, the young finite dimensional cousin of Banach Space theory, functional analysis and classical convexity. We study high, but finite, dimensional objects, where the disorder of many parameters and many dimensions is regularized by convexity assumptions. This workshop is open to all mathematicians.

The summer school will be an introduction to the more algebraic aspects of the theory of automorphic forms and representations. One of the goals will be to understand the statements of the main conjectures in the Langlands programme. Another will be to gain a good working understanding of the fundamental definitions in the theory, such as principal series representations, the Satake isomorphism, and of course automorphic forms and representations for groups such as GL_n and its inner forms.

The purpose of the summer school is to introduce graduate students to the recent developments in the area of dispersive partial differential equations (PDE), which have received a great deal of attention from mathematicians, in part due to ubiquitous applications to nonlinear optics, water wave theory and plasma physics.

Recently remarkable progress has been made in understanding existence and uniqueness of solutions to nonlinear Schrodinger (NLS) and KdV equations, and properties of those solutions. We will outline the basic tools that were developed to address these questions. Also we will present some of recent results on derivation of NLS equations from quantum many particle systems and will discuss how methods developed to study the NLS can be relevant in the context of the derivation of this nonlinear equation.

The theory of dynamical systems has witnessed very significant developments in the last decades, includi​n​g the work of two 2014 Fields medalists, Artur Avila and Maryam Mirzakhani. ​The school will concentrate on the recent significant developments in the field of dynamical systems and present some of the present main streams of research. Two central themes will be those of partial hyperbolicity on one side, and rigidity, group actions and renormalization on the other side.​ ​Other themes will ​include homogeneous dynamics and geometry and dynamics on infinitely flat surfaces (both providing connections to the work of Maryam Mirzakhani), topological dynamics, thermodynamical formalism, singularities and bifurcations in analytic dynamical systems.

McMullen’s g-Conjecture from 1970 is a shining example of mathematical foresight that combined all results available at that time to conjure a complete characterization of face numbers of convex simple/simplicial polytopes. The key statement in its verification is that certain combinatorial numbers associated to geometric (or topological) objects are non-negative. The aim of this workshop is to introduce graduate students to selected contemporary topics in geometric combinatorics with an emphasis on positivity questions. It is fascinating that the dual notions of simple and simplicial polytopes lead to different but equally powerful algebraic frameworks to treat such questions. A key feature of the lectures will be the simultaneous development of these algebraic frameworks from complementary perspectives: combinatorial-topological and convex-geometric. General concepts (such as Lefschetz elements, Hodge–Riemann–Minkowski inequalities) will be developed side-by-side, and analogies will be drawn to concepts in algebraic geometry, Fourier analysis, rigidity theory and measure theory. This allows for entry points for students with varying backgrounds. The courses will be supplemented with guest lectures highlighting further connections to other fields.

We will give an introduction to categorical representation theory, focusing on the example of Soergel bimodules, which is a categorification of the Iwahori-Hecke algebra. We will give a comprehensive introduction to the "tool box" of modern (higher) representation theory: diagrammatics, homotopy categories, categorical diagonalization, module categories, Drinfeld center, algebraic Hodge theory.

The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

In 2017, MSRI-UP will focus on Solving Systems of Polynomial Equations, a topic at the heart of almost every computational problem in the physical and life sciences. We will pay special attention to complexity issues, highlighting connections with tropical geometry, number theory, and the P vs. NP problem. The research program will be led by Prof. J. Maurice Rojas of Texas A&M University.

Students who have had a linear algebra course and a course in which they have had to write proofs are eligible to apply. Due to funding restrictions, only U.S. citizens and permanent residents may apply regardless of funding. Members of underrepresented groups are especially encouraged to apply.

Subfactor theory is a subject from operator algebras, with many surprising connections to other areas of mathematics. This summer school will be devoted to understanding the representation theory of subfactors, with a particular emphasis on connections to quantum symmetries, fusion categories, planar algebras, and random matrices

This workshop will focus on preparing each participant for a successful career as a mathematician at a college or university. Beginning with the hiring process, a thorough discussion of the various elements of the application packet will take place in the context of each participant's materials. Working individually with experienced faculty, participants will review and refine their cover letters, C.V., research, and teaching statements. This will be followed by activities related to the interview. The primary goals of the workshop are to develop an understanding of the hiring process from the institutions' perspective, to refine the application packet, to learn what to expect during the interview process (including the job talk), and to prepare for negotiating salary and start-up packages.

Additional time will be spent on aspects of the pre-tenure years including the development of a research program, writing grant proposals, and mentoring research students. The three-day workshop will consist of one-on-one work with experienced mentors, small group discussions, critique of written materials, plenary sessions, and time for individual work and consultation.

The purpose of the school will be to introduce graduate students to foundational results in commutative algebra, with particular emphasis of the diversity of the related topics with commutative algebra. Some of these topics are developing remarkably in this decade and through learning those subjects the graduate students will be stimulated toward future research.

This workshop will be focused on presenting the latest developments in analytic number theory, including (but not restricted to) recent advances in sieve theory, multiplicative number theory, exponential sums, arithmetic statistics, estimates on automorphic forms, and the Hardy-Littlewood circle method.

The Bay Area Differential Geometry Seminar meets 3 times each year and is a 1-day seminar on recent developments in differential geometry and geometric analysis, broadly interpreted. Typically, it runs from mid-morning until late afternoon, with 3-4 speakers. Lunch will be available and the final talk will be followed by dinner.

Periods are integrals of algebraic differential forms over algebraically-defined domains and are ubiquitous in mathematics and physics. A deep idea, originating with Grothendieck, is that there should be a Galois theory of periods. This general principle provides a unifying approach to several problems in the theory of motives, quantum groups and geometric group theory. This conference will bring together leading experts around this subject and cover topics such as the theory of multiple zeta values, modular forms, and motivic fundamental groups.

Success rates in mathematics as well as recruitment and retention rates in the mathematics pipeline are low at all education levels and are, across predictable demographics, disproportionately low for students who are women, Latin@, Black, American Indian, recent immigrants, emergent bilinguals/multilinguals, and poor. Efforts to address these low rates often focus on programmatic solutions such as creating mentoring or bridge programs to address perceived deficiencies. While these programs achieve some success, evidence suggests that they may not substantially improve students’ subsequent success in mathematics or meaningfully address the ways that students experience mathematics instruction.

The 2017 CIME workshop will focus on observations of mathematics classrooms through the lens of equity. Specifically, we will use observation as a tool for understanding and improving imbalances of access, participation, and power in mathematics teaching and learning. In doing so, we seek to better understand students’ experiences in mathematics classrooms in order to improve academic success, recruitment and retention, and meaningful experiences for historically marginalized populations.

Five questions structure the highly interactive design of the workshop:

What does it mean to create an equitable classroom environment? How can the structure of classroom interactions lead to imbalances of access, identity, and power in mathematics teaching and learning? How can such structures be rebuilt to better serve all students?

How might observations of mathematics instruction help us to identify power dynamics in classrooms? What language is helpful to describe interactions in mathematics classrooms? What might we learn from observations about how culture and identity are developed for some students but not others? What do classroom observations reveal about how instruction supports or discourages engagement in mathematics for students of different backgrounds?

What does it mean to observe interactions in a mathematics classroom with an eye towards equity? What language is helpful to describe interactions in mathematics classrooms? How do we observe and describe interactions among students, between students and mathematics, between students and instructors, and between students and resources (i.e., textbooks, computers, chalkboards, manipulatives)?

What professional experiences can support mathematics instructors to learn how to observe for, describe, interpret, and productively address interactions in the mathematics classroom from the lens of equity? What professional experiences can support mathematics instructors to increase the number of equitable interactions and decrease the number of inequitable ones in their classrooms?

What measures might be useful in tracking our progress in learning to see, describe, interpret, and productively address (in)equitable interactions in mathematics classrooms? What measures and tools might be useful in tracking the impacts on instruction and student learning? How might we develop infrastructure to help with this work (video library, faculty resources, etc.)?